Occasionally you will be given **two linear equations** and asked to solve for x and y. There are numerous ways to do this, including graphing the lines, substitution, and elimination. However, in pre-algebra we will only touch on the first: solving by graphing.

**Solve for x AND y:**

What this question is really asking: find the (x,y) point where these lines meet.

## How to Solve Systems of Equations by Graphing

Graph both lines on the same coordinate grid. Since they are both in slope-intercept form, we can do this by plotting the intercepts then using the slope to find another point.

It is pretty clear where these lines meet, at the point (2, 2), which is our answer!

**Look Out:** be sure to write your answer as a point in (x, y) form.

## Solving Multiple Equations By Graphing Practice:

Solve this system of equations for x and y: | |

The first line is simple to graph, it's just a horizontal line passing through the y-axis at -8. The second line has a y-intercept of 4 and a slope of -4 (or -4/1). These two lines meet at the point (3, -8). | |

Solve this system of equations for x and y: | |

The first line is already in slope-intercept form, so we can easily plot it with a y-intercept of 2 and a slope of ½. The second line needs to be solved for y in order to be in slope-intercept form: | | | *add 3x on each side* | | *rearrange the right hand side* |
| |

Now we can graph it with a y-intercept of 2 and a slope of 3 (or 3/1). They meet at the point (0, 2) | |

Solve this system of equations: | |

This one is very simple. If you really think about it, you won't even need to graph it. However, if you want to see what it looks like, here it is: As you can see, they meet at the point (5, -1). Not a big shocker. | |

Solve this system of equations by graphing:

Solve this system of equations by graphing:

Hint

the y value must be -1

Solve this system of equations by graphing:

Hint

start by solving each equation for y